GEOMETRIC NEWTON TYPE ALGORITHM FOR OPTIMAL RECONSTRUCTION OF STRUCTURE AND MOTION

摘要

To study the structure from motion problem we are led to finding a minimum of a real valued function defined on a product of Riemannian manifolds, e.g., special orthogonal groups and unit sphere. To take advantage of its Riemannian structure we consider Newton algorithm on this manifold. Especially we focus on improving the algorithm to be more robust and faster than the existing Newton algorithm on Riemannian manifolds. For this we exploit the sparse-ness of the Hessian matrix and suggest how to choose the step-size during the optimization procedure, which can be considered as extensions of those for vector space optimization algorithms.